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Block #1,371,777

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2015, 5:47:57 PM Β· Difficulty 10.8106 Β· 5,470,651 confirmations

TWN
Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header
Block Hash
3803bd27cbb0420dcef2d242b114b4ed737507ae347e3d98d5b0129301cc4ade
View on Chainz β†—

Height

#1,371,777

Difficulty

10.810583

Transactions

1

Size

201 B

Version

2

Bits

0acf8263

Nonce

195,993,626

Timestamp

12/16/2015, 5:47:57 PM

Confirmations

5,470,651

Mined by

⛏️ P2SHAFnooow1x4rUpm9BLez5KtnTRWQS2u4KDx

Merkle Root

d5b798c26f7adcf62c886105b577c696f2d0c62f2ad222fd697da39b77bf5380
Transactions (1)
Coinbased5b798c26f7adc…7da39b77bf5380
1 in β†’ 1 out8.5400 XPM110 B
AFnooow1…QS2u4KDx
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

6.848 Γ— 10⁹⁷(98-digit number)
68483803069313032199…63490716337156915199
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
6.848 Γ— 10⁹⁷(98-digit number)
68483803069313032199…63490716337156915199
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.848 Γ— 10⁹⁷(98-digit number)
68483803069313032199…63490716337156915201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
1.369 Γ— 10⁹⁸(99-digit number)
13696760613862606439…26981432674313830399
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.369 Γ— 10⁹⁸(99-digit number)
13696760613862606439…26981432674313830401
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
2.739 Γ— 10⁹⁸(99-digit number)
27393521227725212879…53962865348627660799
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.739 Γ— 10⁹⁸(99-digit number)
27393521227725212879…53962865348627660801
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
5.478 Γ— 10⁹⁸(99-digit number)
54787042455450425759…07925730697255321599
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
5.478 Γ— 10⁹⁸(99-digit number)
54787042455450425759…07925730697255321601
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.095 Γ— 10⁹⁹(100-digit number)
10957408491090085151…15851461394510643199
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.095 Γ— 10⁹⁹(100-digit number)
10957408491090085151…15851461394510643201
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
Rarity
UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,983,838 XPMΒ·at block #6,842,427 Β· updates every 60s
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